Daily Practice · Higher
August 2005 - Higher 5-a-day
Every Higher sheet published in August 2005, with answers. Grades 6-7 - Higher-tier method and manipulation.
Printing for a group?
The batch download puts all 5 tiers' August 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 200511 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 2nd August 200520 beetles are marked and released. Later 54 are caught, of which 6 are marked. Estimate the population.
- 3rd August 2005Write the recurring decimal 0.4141... as a fraction in its simplest form.
- 4th August 2005For the curve y = 30/x, work out y when x = 10, and write down the equation of its vertical asymptote.
- 5th August 2005y is directly proportional to x. When x = 9, y = 54. Work out y when x = 8.
- 6th August 2005A, B and C are points on a circle with centre O. Angle AOC is 110°. Work out angle ABC, where B is on the major arc.
- 7th August 20053 of 9 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 8th August 2005A cumulative frequency graph is drawn for 112 values. What cumulative frequency do you read across from to estimate the lower quartile?
- 9th August 2005A bill is £408 including VAT at 20%. Work out the amount before VAT.
- 10th August 2005Expand and simplify (x + 2)(x - 1)(x + 1).
- 11th August 2005A town's population is 6500 and grows by 8% each year. Work out the population after 4 years, to the nearest whole number.
- 12th August 2005A cone has base radius 3 cm and vertical height 15 cm. Work out its volume, leaving your answer in terms of pi.
- 13th August 200520 students study Spanish and 4 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 14th August 2005A box plot has a minimum of 13 and a maximum of 38. Work out the range.
- 15th August 2005A code is 2 letters (A to Z) followed by 3 digits (0 to 9), and repeats are allowed. How many codes are possible?
- 16th August 2005Make x the subject of y = 8x^2 - 11.
- 17th August 2005A block has volume 180 cm^3 and density 4 g/cm^3. Work out its mass.
- 18th August 2005In triangle ABC, angle A is 68°, angle B is 61° and side a is 6 cm. Use the sine rule to work out side b, to 1 decimal place.
- 19th August 20052 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
- 20th August 2005A box plot has minimum 8, lower quartile 14, median 22, upper quartile 25 and maximum 33. Work out the interquartile range.
- 21st August 2005Work out (9 x 10^10) / (3 x 10^4). Give your answer in standard form.
- 22nd August 2005Factorise x^2 - 36.
- 23rd August 2005x : y = 3 : 8. Write y in terms of x.
- 24th August 2005A right-angled triangle has sides 3 cm, 4 cm and 5 cm. Work out the angle opposite the 3 cm side, to 1 decimal place.
- 25th August 200522 students study Spanish and 6 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
- 26th August 2005A capture-recapture estimate is made of the moth population of a meadow. State one assumption the method relies on.
- 27th August 2005Write the recurring decimal 0.666... as a fraction in its simplest form.
- 28th August 2005A region is defined by y <= 3x + 2. Should the boundary line be solid or dashed, and why?
- 29th August 2005A price rises by 20% and then falls by 10%. Work out the overall percentage change, to 2 decimal places.
- 30th August 2005The point (3, 6) is enlarged by scale factor -3 about the centre (-3, 2). Write down the coordinates of the image.
- 31st August 20052 of 7 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.